The Contextualization Characteristics And Significance Of Rudolf Carnap's Philosophy Of Mathematics

With the turn of linguistics in the early 20 th century,many philosophers attach importance to the study of language.Philosophical studies show the characteristics of language becoming more logical,and the topics concerned by philosophers have also undergone a fundamental change.In particular,people have a wide interest in mathematics and language logic,and take language and logic as the starting point to solve various philosophical problems.Rudolf Carnap is one of the most influential representatives of logical empiricism.His theory of language construction has become the most groundbreaking point of view in the field of linguistic philosophy.But.The study of the philosophical thought of mathematics is relatively lack in the academic circles.This article tries to collate and study the theoretical origin and basic content of Carnap's philosophy of mathematics,to understand the formation and evolution process of his thought,and to grasp the essence of his thought and explore the characteristics of the contextualization of Carnap's philosophy of mathematics.Carnap's dilemma in mathematical philosophy provides a new perspective for solving problems and gives inspiration to methodology in the study of contemporary mathematical philosophy.This paper expounds the contextualization characteristics and significance of Rudolf Carnap's philosophy of mathematics in the following five parts.The first part introduces the theoretical origin of Rudolf Carnap's mathematical philosophy.The first is the distinction between truth and truth in Leibniz's reasoning.It is precisely based on the strict division of these two truths that Rudolf Carnap evolves them into analytical and comprehensive problems in semantics.Secondly,as an important member of the logicism school,including his interest in mathematical philosophy and the formation of the main ideas of linguistic logic,he was deeply influenced by logical empiricism.In addition,he constantly argued with formalism andintuitionism in order to defend the philosophy of logicism.In this process,other important schools of thought were also absorbed,and Enriches one's own theory.In the second and third parts,the main contents and characteristics of Rudolf Carnap's philosophy of mathematics are elaborated in detail.In Rudolf Carnap's philosophy of mathematics,he constructed a complete system of language frame to explain his main ideas,and tried to solve the problems in philosophy of mathematics by constructing a system of conventions.At the same time,the paraphrase rules and semantic analysis are used,and the theory of confirmation of meaning is used as the main content of reductive conclusion.In the process of language frame construction,the characteristics of conventionality,integrity and boundary of language system construction are highlighted.In the fourth part,it is pointed out that when Rudolf Carnap constructs and interprets the philosophical problems with the agreed language,however,due to the limitations of the mathematical philosophy theory itself,the language is faced with the defects of subjectivity and non-communication which can not be overcome.The theory is constructed and solved by the holistic linguistic view with context as the core and the unified analysis method of pragmatics,morphology and semantics on the basis of context,which provides a new way for us to find a new way.In the fifth part,the significance of Rudolf Carnap's mathematical philosophy is analyzed,and the research methods used in Rudolf Carnap's mathematical philosophy are expounded.This new research paradigm will provide new analytical methods and research ideas for the exploration of logicism and the problems existing in mathematical philosophy in the future,and provide a broad research space for the future development of mathematical philosophy.